How do I parent an object to a vertex which is modified by a curve?
Modifiers do affect Vertex parents. (Its in my answer on parenting). So what you are trying to do is completely possible.

Let me start with the setup. I have a curve object (black curved line top left in the image below). The selected object is the one that will be deformed by the curve, lets call it the "bendy bit." The object on the right is the thing I will vertex parent to the bendy bit.


With that out of the way, select the "thing" in your case the buckle, then select the strap (or in my case the bendy bit) that way the bendy bit is the active object. Now Tab into edit mode.

This is how it will look when in edit mode, with another object selected.


Now select three vertices. But not just any three, they have to be near the end with the thing (duh), but they also can not be in a straight line.
See if you select three vertices in a line, that line does not hold enough information to properly convey the orientation to the child object.

So with three vertices selected, like in the image above, press CtrlP > Make Vertex Parent.

Now when you turn on the display of the curve modifier you will see the thing on the end follows properly.  You edit the curve, and everything will update live.




Here is a gif of the whole process, just because people live videos: